5.3 Peak Parameters--A Qualitative Study

To understand why the PCD device has a superior drive capability it helps to find out how the optimal doping level and geometry of the peak change under various operating conditions. Therefore, a qualitative study is carried out which investigates these dependences using the 0.25 $\mu$ m PCD device (Device Generation A).

Additional optimizations are performed with the PCD structure for some representative pairs of $I_{\mathrm{off,max}}$ and $V_{\mathrm{dd}}$ . The resulting optimal parameter sets are listed in Table 5.3 and the doping profiles are depicted in Fig. 5.9 in an arrangement that allows for a convenient comparison of the results.

**Table 5.3:** Results of the qualitative study on the PCD device.
Device		D1	D2	D3	D4	D5
$V_{\mathrm{dd}}$	(V)	0.5	1	1.5	1.5	1.5
$I_{\mathrm{off,max}}$	(pA)	1	1	1	10	100
$I_{\mathrm{on}}$	( $\mu$ A)	4.457	150.1	369.3	405.4	438.9
$N_{\mathrm{sub}}$	(cm $^{-3}$ )	1.15 $\cdot$ 10 $^{16}$	2.72 $\cdot$ 10 $^{16}$	3.04 $\cdot$ 10 $^{16}$	2.54 $\cdot$ 10 $^{16}$	2.29 $\cdot$ 10 $^{16}$
	(cm $^{-3}$ )	0.82 $\cdot$ 10 $^{18}$	1.71 $\cdot$ 10 $^{18}$	2.18 $\cdot$ 10 $^{18}$	2.23 $\cdot$ 10 $^{18}$	2.09 $\cdot$ 10 $^{18}$
	( $\mu$ m)	0.27433	0.24010	0.23977	0.23787	0.23714
	( $\mu$ m)	0.01399	0.01754	0.01907	0.02119	0.02196
$\Delta x$	( $\mu$ m)	0.05738	0.01983	0.00390	0.00283	0.00179
$\sigma_x$	( $\mu$ m)	0.03665	0.01288	0.01141	0.01013	0.01000
$\sigma_y$	( $\mu$ m)	0.01667	0.01000	0.01193	0.01194	0.01158
$x_0+\Delta x+\sigma_x$	( $\mu$ m)	0.36836	0.27281	0.25508	0.25083	0.24893
$y_0+\sigma_y$	( $\mu$ m)	0.03066	0.02754	0.03100	0.03313	0.03354

**Figure 5.9:** Results of the qualitative study on the PCD device.
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It can be observed that for a lower supply voltage the right edge of the doping peak extends towards the drain side ( $x_0+\Delta x+\sigma_x$ increases in Table 5.3) increasing the lateral doping peak length which is in good correspondence with curve (c) in Fig. 5.4. It has been shown in Section 5.2 that the performance improvement resulting from a reduction of the effective channel length of a uniformly doped device which corresponds with the doping peak length in case of the PCD device, can be attributed to the different current-voltage relationships in the weak and strong inversion regimes. It has also been shown that the DIBL effect deteriorates the on-off current ratio, setting a lower limit for the peak length.

The transistor reaches only the moderate inversion regime for $V_{\mathrm{dd}}$ = 1 V which leads to a longer peak. For $V_{\mathrm{dd}}$ = 0.5 V the doping is almost symmetric because the device will stay completely in the weak inversion regime during operation which is indicated by the very low drive current, in this case.

When looking at the transfer curves of the various devices used in this study (Fig. 5.10), it can be seen that the subthreshold slope is better for lower supply voltages. For a higher supply voltage the steep subthreshold characteristic can be traded for improvement of the drive current by further effective gate length reduction. Therefore, the devices D1 and D2 have a steeper subthreshold slope than device D3, and device D1 has a steeper slope than D2.

**Figure 5.10:** The transfer curves of the various devices used in this study (devices D1 to D5). The drain voltage is set to the supply voltage used for each device.
$\resizebox{0.95\textwidth }{!}{ \psfrag{xlabel} [ct][ct] {gate voltage { {$V_{\m... ....5} \includegraphics[width=0.95\textwidth ]{../figures/transfer-study-pcd.eps}}$

For the optimal device the substrate doping $N_{\mathrm{sub}}$ and the peak doping

are reduced for a lower supply voltage delivering the same off-state current, as shown in Table 5.3. This applies also if the allowed off-state current is increased. Then the substrate doping is lowered, too. Additionally, the lateral peak length is slightly reduced for higher leakage currents ( $x_0+\Delta x+\sigma_x$ decreases in Table 5.3) because DIBL is allowed to be higher. However, the optimal PCD devices for different leakage current constraints look very alike, as can be seen in Fig. 5.9.